This melody has no connection to the most famous one on the theme of plums,
Three Repetitions of the Tune Plum Blossom
(Meihua Sannong). As a melody title Meishao Yue can be found in a Song dynasty
Melody List, and has been attributed to Guo Chuwang (see comment). However, there is no way to know whether that melody had any connection to the present one.

Tablature for the present melody survives in only one handbook, Xilutang Qintong (1525),4 which connects the melody to a poem by the early Song dynasty painter, calligrapher and poet Lin Bu (967-1028).5 Lin Bu was particularly famous as a recluse who claimed that he considered plum trees his wife and pet cranes his children, and so never married. A lifelong resident of Hangzhou, he spent 20 years on Solitary Mountain, an island in Hangzhou's West Lake; a gravesite and neighboring Releasing Cranes Pavilion are said to mark the spot.6

When everything has faded they alone shine forth
encroaching on the charms of smaller gardens
their scattered shadows fall lightly on clear water
their subtle scent pervades the moonlit dusk
snowbirds look again before they land
butterflies would faint if they but knew
thankfully I can flirt in whispered verse
I don't need a sounding board or winecup

This poem also serves as lyrics for a melody called Plum Blossoms (Mei Hua), surviving in several Japanese handbooks though quite likely brought there from China.9 Chinese have long prized plum trees and their blossoms. They symbolize winter because blossoms can appear even while there is still snow on the ground; and purity because of these white blossoms.

The Fleeing Immortal (Lin Bu) built a cottage on Solitary Mountain (in Hangzhou's West Lake). At night he intoned as he leaned out his small window and saw the moon struggling to get free of the clouds. As a result we have this melody. It has beautiful sounds, like the phrases "scattered shadows" and "subtle scent" (from Lin Bu's poem).

3.The Poet Lin Bu Wandering in the MoonlightThis painting, by 杜堇 Du Jin (Ming dynasty;
Wiki), is
#1954.582 in the Cleveland Museum of Art. Other paintings on this theme, and thus of particular relevance to this melody include:

Honolulu Academy of Arts, 馬遠 Ma Yuan (active 1190-1230), A Gentleman in his Garden.
Comments on the painting suggest that "perhaps it is Lin Bu looking at the plum trees".

Shanghai Museum, 杜堇 Du Jin, 梅下橫琴圖 Playing the Qin Underneath a Plum Tree (I don't know how accurate the color is in
this reproduction).

5.Lin Bu (967-1028)14856.234 林逋 "From Qiantang (Hangzhou), literary name 君復 Junfu (no mention of a hao or of 逋仙 Bu Xian, lit., 'fleeing immortal', using the 'bu' of 'Lin Bu', meaning 'flee'). In tranquility loving ancient things, he did not seek fame or fortune, instead becoming a recluse on West Lake's Solitary Mountain (孤山 Gu Shan). For 20 years he remained there without needing to go into the city. He was skilled at calligraphy and painting, and expert with his poetry." Translations of Lin Bu's poems are included in several anthologies.
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See also a view from the gravesite. Gushan Island in Hangzhou's West Lake has, on the side facing the main lake, the original premises of the Zhejiang Museum. On the hill behind the museum are a number of artists' studios, and on the opposite side of the hill is a gravestone marked as that of Lin Bu (967-1028), known for his love of plum trees and cranes. A nickname for the island is said to have been Plum Island (梅嶼 Mei Yu) for its many plum trees, particularly around the grave of Lin Bu; and next to the grave is a Releasing Cranes Pavilion (放鶴亭 Fang He Ting). The gravesite is quite peaceful when visitors are not playing karaoke in the pavilion.
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7.How Plum Flowers Embarrass a Garden (山園小梅 Shan Yuan Xiao Mei), by 林逋 Lin BuThis poem (the title is sometimes also translated as Small Plum Tree in my Mountain Garden) was included in what was perhaps the most famous early anthology of poetry since the Book of Songs and the Songs of Chu, the 千家詩 Poems of 1,000 Masters, a collection of 224 poems by about 100 masters of the Tang and Song dynasties.
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8.How Plum Flowers Embarrass a Garden, a translation by Red PineThe translation above was included with permission. See Red Pine (trans.), Poems of the Masters; Port Townsend, Copper Canyon Press, 2003, p.453. The original text of the poem (p.452) is as follows ,